---
title: "Using the robsel package"
#output: rmarkdown::html_vignette
output: pdf_document
vignette: >
  %\VignetteIndexEntry{Using RobSel}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

This vignette illustrate the basic usage of the `robsel` package to estimate of the regularization parameter for Graphical Lasso.

## Data
We use a 100-by-5 matrix from generate from normal distribution.
```{r}
x <- matrix(rnorm(100*5),ncol=5)
```


## Using `robsel` functions

### Estimate of the regularization parameter for Graphical Lasso
The function `robsel` estimates $\lambda$, a regularization parameter for Graphical Lasso at a prespecified confidence level $\alpha$.
```{r}
library(robsel)
lambda <- robsel(x)
lambda
```

### Graphical Lasso algorithm with $\lambda$ from Robust Selection
The function `robsel.glasso` returns estimates a sparse inverse covariance matrix using Graphical Lasso with regularization parameter estimated from Robust Selection
```{r}
A <- robsel.glasso(x)
A
```

### Use RobSel with multiple prespecified confidence levels
We can use multiple $\alpha$ simultaneously with Robust Selection
```{r}
alphas <- c(0.1, 0.5, 0.9)
lambdas <- robsel(x, alphas)
lambdas
```

```{r}
robsel.fits <- robsel.glasso(x, alphas)
robsel.fits
```